A woman has been questioned by police and could face a hate crime prosecution after she waved a banner at Belfast’s Pride parade reading “Fuck the DUP”.

In a case that could have consequences for free speech and the right to offend across the UK, the Police Service of Northern Ireland (PSNI) says it will pass a file to the region’s public prosecution service (PPS) after Ellie Evans, 24, held up the placard at the August parade to protest against the party’s policies on gay marriage.

The investigation was prompted by a complaint from DUP politician Jim Wells, who told the Guardian that the slogan constituted “incitement to hatred and potential public disorder”.

Evans, originally from Essex, confirmed that two PSNI detectives questioned her under caution on Monday. She said that in a later phone call she was told that the PPS would decide whether she should be prosecuted for a hate crime or a breach of public order.

“I said to them: ‘Why?’” she said. “To say this placard and its message was a hate crime is insulting to all those many LGBT people in Northern Ireland who are affected by genuine hate crimes on a daily basis.

“How many people have the PSNI arrested here for the burning of effigies of nationalist politicians or flags of that tradition on loyalist bonfires? I just can’t believe they have referred this to the PPS. I just thought it would be a laugh.”

Evans said that she held up the banner to highlight how the party that props up Theresa May’s government blocks gay marriage equality in Northern Ireland.

The charity worker, who has lived in Northern Ireland for two years, was questioned at a central Belfast police station after a detective visited her at home on 5 October.

“I got a knock on my door and there was a plainclothes PSNI detective standing there,” she said. “He said that they would like me to come in to answer a few questions then gave me his details and we arranged a time.

“So on Monday evening I took a lawyer with me and I had to speak to two detectives. They asked me questions like did I think the F word was offensive, and if I thought it was appropriate to display this word in a public place where children were around. They asked if I was trying to be provocative and what my intentions were, which should have been obvious.

“They were like questions you would expect to be asked by a teacher at school over graffiti scrawled in a toilet or a cloakroom. The whole thing was weird.”

She told the PSNI officers she was simply doing her bit for the campaign to promote marriage equality in Northern Ireland. The region is the only part of the UK where same-sex couples cannot be married. This is because the DUP, now shoring up the minority Conservative government in Westminster, has consistently used a parliamentary veto in the Northern Ireland assembly to veto legislation to legalise same-sex marriages.

The DUP politician who first complained about Evans’s placard back in August at Pride was unapologetic about his actions.

Jim Wells, the DUP’s assembly member for South Down, previously resigned from the National Trust, for whom he worked for a decade, over its participation in the Pride parade.

Wells told the Guardian it had been overlooked that a slogan such as “Fuck The DUP” breached the strict rules concerning marching in Northern Ireland as set down by the Parades Commission – the body that adjudicates on controversial demonstrations in the region.

Wells, who avoids swearing, said: “If someone at an Orange Order march held up a banner stating, ‘eff Sinn Féin’ or if someone from a religious group held up a placard with the slogan, ‘eff LGBT’ at parade that would be a clear breach of the Parades Commission’s rules barring offensive slogans.

“This ‘eff The DUP’ placard is exactly the same,” he went on. “I don’t mind if they hold up banners criticising the DUP, saying we are idiots or whatever. But to use a swearword is tantamount to an incitement to hatred and potential public disorder.

“You may not agree with the DUP but we represent 300,000 people and are the largest political party in this province. They deserve some respect free from offence. As a unionist I would find it unacceptable and offensive if anyone used that same slogan, that same swearword against any of the nationalist parties here.”

LGBT campaigners expressed their concern at PSNI’s approach. “We would ask that PSNI detail their reasoning as to why they felt there was sufficient evidence of a crime being committed to warrant questioning,” said Gavin Boyd, policy and advocacy manager at the Rainbow Project.

“We would also ask PSNI whether additional weight was given to the complaint because it came from an elected politician and whether any anti-Pride protesters have ever been questioned about the content of their placards.”

A spokesperson for the PSNI said: “When any complaint is received PSNI will examine the report and speak to all relevant parties to establish if any offence has been committed. In relation to this specific case, inquiries are ongoing and a file will be submitted to the PPS in due course.”

• This article was amended on 18 October 2017 to correct a quote mistakenly attributed to Gavin Boyd.